Suppose that a machine requires daily maintenance, and let M(t) be the annual rate of maintenance expense at time t. Suppose that the interval 0 ≤ t ≤ 2 is divided into n subintervals, with endpoints t₀ = 0, t₁,. . . , t_n = 2.

(a) Give a Riemann sum that approximates the total maintenance expense over the next 2 years. Then, write the integral that the Riemann sum approximates for large values of n.

(b) Give a Riemann sum that approximates the present value of the total maintenance expense over the next 2 years using a 10% annual interest rate compounded continuously. Then, write the integral that the Riemann sum approximates for large values of n.